Spatial multiplexing is a transmission scheme that can exploit multiple antennas at both a base transceiver station and at subscriber units to increase the bit rate in a wireless radio link with no additional power or bandwidth consumption. Under certain conditions, spatial multiplexing offers a linear increase in spectrum efficiency with the number of antennas. For example, if three antennas are used at the transmitter and the receiver, the stream of possibly coded information symbols is split into three independent sub-streams. These sub-streams occupy the same channel of a multiple access protocol. Possible same channel multiple access protocols include a same time slot in a time-division multiple access protocol, a same frequency slot in frequency-division multiple access protocol, a same code sequence in code-division multiple access protocol or a same spatial target location in space-division multiple access protocol. The sub-streams are applied separately to the transmit antennas and transmitted through a radio channel. Due to the presence of various scattering objects in the environment, each signal experiences different multi-path propagation.
The composite signals resulting from the transmission are finally captured by multiple receiving antennas with random phase and amplitudes. At the multiple antenna receiver, a spatial signature of each of the received signals is estimated. Based on the spatial signatures (spatial signature and channel estimate are synonymous), a signal processing technique can be applied to separate the signals, recovering the original data sub-streams.
A type of spatial multiplexing is collaborative spatial multiplexing (CSM). CSM include multiple subscribers sharing a transmission channel for uplink transmission to a multiple antenna base station. The base station can characterize the transmission channels between the subscribers and the base station through the use of pilot tones within the transmission signals from the subscribers. In a mobile environment, the channel estimates can become inaccurate as subscribers move. The inaccuracies are primarily due to errors in the estimate of timing and frequency offset between the transmitter and the receiver. These offset may be created due to motion (Doppler), temperature, propagation delay, aging and other factors (such as, clocks of the transmitters and receivers).
It is desirable to improve estimates of transmission channels between base stations and mobile subscribers. Additionally, it is desirable to reduce the effects of frequency offset errors.